Midterm05

Midterm05 - Department of Economics ECONOMETRICS I Fall...

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ECONOMETRICS I Fall 2005 – Tuesday, Thursday, 1:00 – 2:20 Professor William Greene Phone: 212.998.0876 Office: KMC 7-78 Home page:www.stern.nyu.edu/~wgreene Office Hours: Open Email: wgreene@stern.nyu.edu URL for course web page: www.stern.nyu.edu/~wgreene/Econometrics/Econometrics.htm Midterm 1. In the classical regression model, y i = x i1 ′ β 1 + x i2 ′ β 2 + ε i , i = 1 ,…,n , E[ε i | X ] = 0, Var[ε i | X ]=σ 2 ; X 1 is K 1 variables and X 2 is K 2 variables. There are two possible estimators of β 1 , the first K 1 coefficients in the “long regression” of y on X 1 and X 2 and the K 1 coefficients in the short regression of y on X 1 . Let X = [ X 1 , X 2 ]. We will assume that plim[(1/n) X X ] = Q , a positive definite matrix. a. [5 points] Assume that plim[(1/n) X 1 X 2 ] ≠ 0 . Is either estimator unbiased? Is either estimator consistent? b. [5 points] Assume that plim[(1/n) X 1 X 2 ] = 0. Is either estimator unbiased? Is either estimator consistent? c. [5 points] Explain the difference between consistency and unbiasedness. Does either imply the other? Explain. d. [5 points] Suppose the assumption in a. is correct. The estimator we will use is the following: We will compute the long regression. F is the conventional F statistic for testing the null hypothesis that β 2 is zero. If F > 2, we will use the long estimator. If F < 2, we will use the short estimator. Is the estimator consistent? Unbiased? (Hint, you can think this one through to an answer without deriving a probability limit.) 2. The regressions for this problem are based on a sample of 27,326 observations, a survey of health care system usage taken in Germany over 7 years in the 1990s. The four regressions below are income equations based on the model Income = β 1 + β 2 Educ + β 3 Educ 2 + β 4 Married + β 5 Female + β 6 Hhkids + ε Department of Economics
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Educ is measured by years of schooling. Married and Hhkids are dummy variables for marital status and whether there are kids in the household, and Female = 1 for women, 0 for men. In the first regression, the dummy variable FEMALE is included; in the second, it is omitted. The third regression is the same as the second, for women only; the fourth is the same as the second, but for men only. a . [5 points] How would you test the hypothesis that all coefficients in the first model except the constant term are equal to zero? Carry out the test. b. [5 points] The coefficient on FEMALE in the first regression is a measure of the difference between men and women with everything else held constant. The underlying null hypothesis is that the income determination mechanism is the same for men and women. The alternative hypothesis is that the income determinations are the same, except there is a constant difference
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This note was uploaded on 01/05/2012 for the course B 30.3351 taught by Professor Williamgreene during the Fall '11 term at NYU.

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Midterm05 - Department of Economics ECONOMETRICS I Fall...

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